Eddy currents are one of the main causes of deleterious cross-talk within hybrid MRI scanners such as (IGRT-MRI) Image Guided Radiotherapy-MRI or PET-MRI systems. Currents induced in the conducting parts of scanners produce acoustic noise, power heating, magnetic field asymmetries. In this paper we present a new fast and efficient eddy current simulation method which combines current densities expressed as normalized Fourier series and linear basis functions. The new method is capable of accurately simulating currents induced in thick cylinders of finite length (such as a cryostat) and thin surfaces of arbitrary shape by coils of arbitrary geometry.